CBSE Questions for Class 9 Maths Polynomials Quiz 13 - MCQExams.com

If the sum of two roots of the equation $$\displaystyle x^3 px^2 + qx r = 0$$ is zero , then
  • pq = r
  • qr = p
  • pr = q
  • pqr = 1
If $$f(x)={ 4x }^{ 4 }-{ ax }^{ 3 }+{ bx }^{ 2 }-cx+5$$ (a, b, c $$\in $$ R) has four positive real zeros $${ r }_{ 1 },{ r }_{ 2 },{ r }_{ 3 },{ r }_{ 4 }$$ such that $$\frac { { r }_{ 1 } }{ 2 } +\frac { { r }_{ 2 } }{ 4 } +\frac { { r }_{ 3 } }{ 5 } +\frac { { r }_{ 4 } }{ 8 } =1$$, then a is equal to 
  • 19
  • 20
  • 21
  • 22
The equation $${\left( {x - 3} \right)^9} + {\left( {x - {3^2}} \right)^9} + {\left( {x - {3^3}} \right)^9} + .... + {\left( {x - {3^9}} \right)^9} = 0\;has:$$
  • all the roots are real
  • One real and 8 imaginary roots
  • real roots namely $$x = 3,\;{3^2},{.....3^9}$$
  • Five real and 4 imaginary roots
The roots of the equation $$ax^3 + bx^2 - x + 1=0$$ are real, distinct and are in H.P., then
  • $$b$$ $$\epsilon$$ $$(-\infty,\frac{1}{3})$$
  • $$a$$ $$\epsilon$$ $$(-\frac{1}{27},\infty)$$
  • $$27a + 9b=2$$
  • None of these
The roots of $$6x^{4}-35x^{3}+62^{2}-35x+6=0$$ are.......
  • 2,-1/2,-1/3,3
  • 2,1/2,3,1/3
  • -2,-1/2,-3,-1/3
  • 2,1/2,-3,-1/3
If $$p,\quad q,\quad r,\quad s\quad \in R$$, then equation $$({ x }^{ 2 }+{ px }+{ 3 }q)({ -x }^{ 2 }+rx+q)({ -x }^{ 2 }+sx-2q)=0$$ has
  • 6 real roots
  • atleast two real roots
  • 2 real and 4 imaginary roots
  • 4 real and 2 imaginary roots
The sum of the roots of the equation $$cot-1x-1(x+2)=150$$ is
  • 0
  • 1
  • 2
  • -2
If $$1,-2,3$$ are the roots of $${ x }^{ 3 }-b{ x }^{ 2 }+ax+6=0$$, then a=
  • $$-5$$
  • $$5$$
  • $$2$$
  • none of these
The expansion $$\frac{1}{{\sqrt {4x + 1} }}\left[ {{{\left[ {\frac{{1 + \sqrt {4x + 1} }}{2}} \right]}^7} - {{\left[ {\frac{{1 - \sqrt {4x - 1} }}{2}} \right]}^7}} \right]$$ is a polynomial in x of degree 
  • 7
  • 6
  • 4
  • 3
If roots of equation $$8x^3 -14x^2+7x-1 =0$$ are in geometric progression, then roots are 
  • $$3,6,8$$
  • $$1,2,4$$
  • $$2,4,8$$
  • $$1,1/2,1/4$$
If $$a,\beta ,y$$ are the roots of equation $${ x }^{ 3 }+2x-5=0$$ and if equation $${ x }^{ 3 }+{ bx }^{ 2 }+cx+d=0\quad has\quad roots\quad 2a+1.\quad 2\beta +1,\quad 2y+1.$$ then value of $$\left| b+c+d \right| $$ is (where b,c,dd are coprime ) -
  • 41
  • 39
  • 40
  • 43
The expression $${ \left[ x+{ \left( { x }^{ 3 }-1 \right)  }^{ 1/2 } \right]  }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right)  }^{ 1/2 } \right]  }^{ 5 }$$ is a polynomial of degree
  • 5
  • 6
  • 7
  • 8
If a is a non-real root of $${ x }^{ 6 }=1$$, then $$\dfrac { { a }^{ 5 }{ a }^{ 3 }+a+1 }{ { a }^{ 2 }+1 } $$ is
  • $${ a }^{ 2 }$$
  • 0
  • $${ -a }^{ 2 }$$
  • a
If one root of $$32 x ^ { 3 } - 48 x ^ { 2 } + 22 x - 3 = 0$$ is equal to half of the sum of the other two roots , then the roots are 
  • $$1 / 4,1 / 2,3 / 4$$
  • $$4,2,4 / 3$$
  • $$3,4,5$$
  • $$2.3 .5/2$$
The expression $$(x+(x^4-1)^{1/2})^4 + (x-(x^4-1)^{1/2})^4$$ is a polynomial of degree
  • 8
  • 6
  • 4
  • 2
number of real roots of the equation
$$\sqrt { x } +\sqrt { x-\sqrt { 1-x }  } =1\quad is$$
  • 0
  • 1
  • 2
  • 3
Find the value of  $$\dfrac { 10.5 \times 10.5 - 15 \times 10.5 + 7.5 \times 7.5 } { 10.5 - 7.5 }.$$ 
  • $$17$$
  • $$3$$
  • $$6$$
  • $$22$$
If $$\alpha ,\beta ,\gamma $$ are roots of $$7{ x }^{ 3 }-x-2=0$$ then find the value of $$\sum { \left( \dfrac { \alpha  }{ \beta  } +\dfrac { \beta  }{ \alpha  }  \right)  } $$
  • 1
  • 2
  • -3
  • -4
The HCF of two ploynomials $$A$$ and $$B$$ using long division method was found to be $$2x + 1$$ after two steps . The fisrt two quotient obtained are $$x$$ and $$(x + 1)$$ . Find $$A$$ and $$B$$ . Given that degree of $$A$$ > degree of $$B$$ is 
  • $$A = 2x^3 + 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$
  • $$A = 2x^3 - 3x^2 + x - 1 $$ ; $$B = 2x^2 - 3x - 1 $$
  • $$A = 2x^3 + 3x^2 - 3x - 1 $$ ; $$B = 2x^2 - 3x + 1 $$
  • $$A = 2x^3 + 3x^2 + 3x + 1 $$ ; $$B = 2x^2 + 3x + 1 $$
The degree of the expression
$$(1+x)(1+{ x }^{ 6 })(1+{ x }^{ 11 })........(1+{ x }^{ 101 })$$
is
  • 1081
  • 1061
  • 1071
  • 1091
The root of the equation $${ X }^{ 4 }-1=0$$ are;
  • 1,1,i,-i
  • 1,-1,i,-i
  • 1,-1,$${ \omega ,\omega }^{ 2 }$$
  • none of these
The expression $$\frac { 1 }{ \sqrt { 4x+1 }  } \left[ \left[ \dfrac { 1+\sqrt { 4x+1 }  }{ 2 }  \right] ^{ 7 }-\left[ \dfrac { 1-\sqrt { 4x+1 }  }{ 2 }  \right] ^{ 7 } \right] $$ is a polynomial in x degree- 
  • 7
  • 5
  • 4
  • 3
0:0:1


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